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view toolbox/parter.m @ 2:c124219d7bfa draft
Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author | Antonio Pino Robles <data.script93@gmail.com> |
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date | Thu, 07 May 2015 18:36:24 +0200 |
parents | 8f23314345f4 |
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function A = parter(n) %PARTER Parter matrix - a Toeplitz matrix with singular values near PI. % PARTER(N) is the matrix with (i,j) element 1/(i-j+0.5). % It is a Cauchy matrix and a Toeplitz matrix. % At the Second SIAM Conference on Linear Algebra, Raleigh, N.C., % 1985, Cleve Moler noted that most of the singular values of % PARTER(N) are very close to PI. An explanation of the phenomenon % was given by Parter; see also the paper by Tyrtyshnikov. % % References: % The MathWorks Newsletter, Volume 1, Issue 1, March 1986, page 2. % S.V. Parter, On the distribution of the singular values of Toeplitz % matrices, Linear Algebra and Appl., 80 (1986), pp. 115-130. % E.E. Tyrtyshnikov, Cauchy-Toeplitz matrices and some applications, % Linear Algebra and Appl., 149 (1991), pp. 1-18. A = cauchy( (1:n)+0.5, -(1:n) );